Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization

Authors:
G. H. Keetels;H. J. Clercx;G. J. Heijst
Affiliations:
Department of Physics, Eindhoven University of Technology, The Netherlands;Department of Physics, Eindhoven University of Technology, The Netherlands and Department of Applied Mathematics, University of Twente, The Netherlands;Department of Physics, Eindhoven University of Technology, The Netherlands
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Year:
2007

Citing 2
Cited 0

A spectral solver for the Navier-Stokes equations in the velocity-vorticity formulation for flows with two nonperiodic directions

Journal of Computational Physics
Fourier spectral and wavelet solvers for the incompressible Navier-Stokes equations with volume-penalization: Convergence of a dipole-wall collision

Journal of Computational Physics

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Abstract

In this study we use a fast Fourier spectral technique to simulate the Navier-Stokes equations with no-slip boundary conditions. This is enforced by an immersed boundary technique called volume-penalization. The approach has been justified by analytical proofs of the convergence with respect to the penalization parameter. However, the solution of the penalized Navier-Stokes equations is not smooth on the surface of the penalized volume. Therefore, it is not a prioriknown whether it is possible to actually perform accurate fast Fourier spectral computations. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole-wall collision as a test case. It is found that Gibbs oscillations have a negligible effect on the flow evolution. This allows higher-order recovery of the accuracy on a Fourier basis by means of a post-processing procedure.